Apair of fair dice is rolled once. suppose that you lose $7 if the dice sum to 10 and win $11 if the dice sum to 11 or 2. how much should you win or lose if any other number turns up in order for the game to be fair? to keep the game fair, you should if the dice sum to any other number. (do not round until the final answer. then round to the nearest cent as needed.)

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4